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A quantum group covariant extension of the chiral parts of theWess-Zumino-Novikov-Witten model on a compact Lie group G gives rise to twomatrix algebras with non-commutative entries. These are generated by "chiralzero modes" which combine in the 2D model into "Q-operators" which encodeinformation about the internal symmetry and the fusion ring. We review earlierresults about the SU(n) WZNW Q-algebra and its Fock representation for n=2 anddisplay the first steps towards their generalization to higher n.

On the 2D zero modes' algebra of the SU(n) WZNW model